Achieving epitaxial growth and fabrication of high-performance optoelectronic devices (i.e., III-V devices) on silicon substrates has been a goal of the semiconductor industry for decades. A major challenge has been to overcome the large lattice-mismatch and thermal-expansion differences between these two fundamentally different material systems. Various methods have been used in the past to demonstrate III-V-based lasers on Si substrates, for example utilizing very thick (˜10 micrometer (μm)) epitaxial buffer layers (see “Monolithic integration of room-temperature cw GaAs/AlGaAs lasers on Si substrates via relaxed graded GeSi buffer layers,” Michael B. Groenert, Christopher W. Leitz, Arthur J. Pitera, and Vicky Yang, Journal of Applied Physics 93 362 (2003)) or utilizing wafer bonding between a Si wafer and epitaxial layers grown on a III-V substrate (see “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Alexander W. Fang, Hyundai Park, Oded Cohen, Richard Jones, Mario J. Paniccia, and John B, Bowers, Optics Express, Vol 14, Issue 20, pp. 9203-9210 (2006)), However, these methods may have disadvantages from either an economic or a technical standpoint. It may be desirable to avoid both (a) thick epitaxial layers that may be time-consuming to grow, and may suffer from thermal mismatch problems, and (b) bonding between Si and III-V wafers that can suffer from poor yield, thermal mismatch problems, and a lack of commercially available III-V substrates compatible with the Si substrates used today in leading-edge manufacturing. Particularly desirable is an epitaxial solution that can (a) achieve substantial elimination of defects arising from lattice mismatch with no more than about 1 μm of growth, and (b) manage large degrees of thermal mismatch (i.e., mismatch between the thermal expansion coefficients of the substrate and the epitaxial layers).